That was quite a long time I hadn't heard of asymptotically to zero
. I think I got it: actually it never gets to zero but infinite close to zero.
This is incorrect. The block subsidy (new coin creation) drops to zero after block 6,929,999. The subsidy amount is cut in half and truncated to the nearest 0.00000001 BTC every 210,000 blocks. After 210,000 blocks with a subsidy of 0.00000001 BTC, that amount is cut in have and truncated to 0.00000000.
Miners will just stop mining because the cost of finding will surpass the value of the reward. However, the latter can be countered as the cost of mining (in USD) will not increase as much as the reward for finding (in Bitcoins), because of the limit restriction Bitcoins can only go up.
So long as bitcoin exists and is used, mining will not stop. The block reward consists of the sum of the block subsidy AND the total of all the transaction fees of all the unconfirmed transactions the miner includes (confirms) in the block. As bitcoin gains popularity, the value of the transaction fees is expected to increase. Meanwhile the block subsidy will be cut in half aproximately every 4 years. At the moment the block subsidy is the majority of the reward, and the fees are only a small percentage. Eventually, the fees will be the majority of the reward and the subsidy will be only a small percentage. Perhaps at that time people will stop calling them "miners" and instead call them "transaction processors", but the work they do will be the same.
Let's replace 'new bitcoin' with, eg lightcoin. The altcoins are using the same infrastructure as bitcoins (some with minor changes). So, the altcoins are filling in the demand of the community for a 'new bitcoin'?
Exactly. Each altcoin is already an attempt to provide a bitcoin-like cryptocurrency with a different set of protocol rules. If any of them succedd long term, then that success will prove the theory behind the protocol rules. In the meantime, bitcoin's set of rules appears to be the most successful so far.